Explain what it means for two random variables to be independent, both mathematically and in layman’s terms. If we assume two random variables are independent, what does it allow us to simplify?

A recent survey of post-secondary education students in Canada revealed that 75% are confident in their ability to manage their finances. You are to randomly pick 35 post-secondary education students across the country, and ask each the following question: maga LEDEL You have defined the random variable X to represent the number, out of 35 post-secondary students chosen, who respond YES. P(X= 24) (a) What is the probability that 24 of these post-secondary students respond YES? Are you confident in your ability to manage your finances? P(14 < X < 19) (b) What is the probability that between 14 and 19 of these students will respond YES? E(X) = x (use four decimals in your answer) SD(X)=ox= (c) How many of the 35 post-secondary students would you expect to respond YES? Find the standard deviation as well. (use four decimals in your answer) (use two decimals in your answer) (use two decimals in your answer) (d) What can you say about the distribution of the X? Select the most appropriate…

In each of the examples that follow, determine what value the random variable would assign to the specific outcome listed.   You have some number of coins in your pocket, and you choose two at random. The random variable ZZ assigns the value of the coins in cents to each outcome. What value is assigned when you draw out a quarter and a dime? A coin is flipped three times. YY is a random variable that assigns 3 times the number of heads flipped minus 2 times the number of tails flipped. What number is assigned to HHT? A person picks a number between 1 and 272820. The random variable ZZ assigns the 0 to an even number and 1 to an odd number. What number is assigned to 270221?

A believer in the "random walk" theory of stock markets thinks the value of an index of stock prices has a 0.6 probability of rising in any year. The change in the value of the index in any given year is not affected by whether it rose or fell in earlier years. You plan to record the value for the index in each of the next eight years. Let the random variable, X, represent the number of years (out of the next 8 years) in which the value of the index rises. a) If X is distributed according to the binomial probability distribution, what are the values for n and p?o b) What are the possible values X can take, or equal? QMETH 201, Homework 3 c) Calculate the probability X = 30 d) Calculate the expected value for X. e) Calculate the standard deviation for X. 4